\nThat night, I talked to Xiaoyin about a book I owned when I was in her grade (third grade): The Won\u00adder\u00adful 9. It was the only book I ever bought from ele\u00admen\u00adtary school to mid\u00addle school, so it left a deep impres\u00adsion on me.
\n
\n
\nI said that after read\u00ading this book, I was sur\u00adprised to find that the sum of all nat\u00adur\u00adal num\u00adbers with two dig\u00adits or more that can be divid\u00aded by 9 can also be divid\u00aded by 9. For exam\u00adple, 9801, 9+8+0+1=18
\n, because 18 is divis\u00adi\u00adble by 9, and so is 9801. Fur\u00adther\u00admore, if the sum of the num\u00adbers can\u00adnot be divid\u00aded by 9, the remain\u00adder is the remain\u00adder of the orig\u00adi\u00adnal num\u00adber divid\u00aded by 9. This prin\u00adci\u00adple can sim\u00adpli\u00adfy cal\u00adcu\u00adla\u00adtions for many prob\u00adlems.
\n
\n
\nMy daugh\u00adter was very curi\u00adous about this. So we ran\u00addom\u00adly thought of some num\u00adbers to test it out, and of course the results came true. I thought we could stop here, but she kept ask\u00ading me -
\n
\n
\nWhy is this?
\n
\n
\nOops, if this were a sto\u00adry, I could tell her, \u201cIt\u2019s just a sto\u00adry.\u201d But this is math, so we have to go to the trou\u00adble of prov\u00ading it.
\n
\n
\nI took a large piece of white paper (if it was small\u00ader, I prob\u00ada\u00adbly would\u00adn\u2019t be able to cal\u00adcu\u00adlate it) and said I would cal\u00adcu\u00adlate it for you.
\n
\n
\nLet\u2019s start with a four-dig\u00adit num\u00adber. For exam\u00adple, let\u2019s say there is a four-dig\u00adit num\u00adber, and the dig\u00adits of each dig\u00adit are A, B, C, and D.
\n
\n Assump\u00adtion: A + B
\n+ C + D = 9M (which means it is divis\u00adi\u00adble by 9)
\n
\n
\nThe num\u00adber is actu\u00adal\u00adly: 1000A + 100B + 10C + D. Let me try to break it down:
\n
\n (1+999)A
\n+ (1+99)B + (1+9)C + D
\n = (A + B
\n+ C + D) + 999A + 99B + 9C
\n = 9M +
\n9(111A + 11B + C)
\n = 9(M +
\n111A + 11B + C)
\n
\n
\nHow about it? Now you see clear\u00adly, this num\u00adber must be divis\u00adi\u00adble by 9, right?
\n
\n
\nI thought I\u2019d explained the math clear\u00adly enough, but my daugh\u00adter looked bewil\u00addered. She said it seemed like it, but she just could\u00adn\u2019t fig\u00adure out what ABCD meant! Her moth\u00ader then joined in the fun, look\u00ading at us with a gloat\u00ading expression\u2014this was the real kick\u00ader; did\u00adn\u2019t you see I was sweat\u00ading pro\u00adfuse\u00adly?
\n
\n
\nI was real\u00adly pushed to the lim\u00adit, so I said to Xiaoyin, let\u2019s throw away all ABCD and think of a four-char\u00adac\u00adter idiom for me. Xiaoyin hes\u00adi\u00adtat\u00aded for a moment and blurt\u00aded out: \u201cShit and fart\u201d, and the three of us burst out laugh\u00ading. Okay, \u201cShit and fart\u201d will work. Let\u2019s look at it again:
\n
\n Assump\u00adtion: Poop + Shit
\n+ fart + fart = 9 mmm (this should make it clear\u00ader!)
\n
\n
\nThis four-dig\u00adit num\u00adber is: 1000 poops + 100 shits + 10 flat\u00adu\u00adlences + 1 fart (okay, that\u2019s it)
\n
\n Breaks down to:
\n (1+999)
\n+ (1+99) shit + (1+9) fart +
\n = (Poop + Shit
\n+ fart + 999 shit + 9 fart
\n = 9 hmmm +
\n9 (111 poop + 11 shit + release)
\n = 9(hmm +
\n111 poop + 11 shit + release
\n
\n
\nHow about it, is it clear enough this time?
\n
\n
\nMy daugh\u00adter laughed all the way and said that she final\u00adly under\u00adstood it. How\u00adev\u00ader, she real\u00adly could\u00adn\u2019t hold it in any longer, so she real\u00adly cov\u00adered her stom\u00adach and uri\u00adnat\u00aded\u2026
\n
\n
\nIt was the first time I dis\u00adcov\u00adered that math\u00ade\u00admat\u00adics has such mag\u00adi\u00adcal pow\u00ader!
\n
\nXiaoy\u00adin\u2019s father\u2019s evening diary, Feb\u00adru\u00adary 23, 2009<\/p>","protected":false},"excerpt":{"rendered":"
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